Finite Group Databasebeta

← #29574870

Subgroups — #29574870

Order 15616.

578 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455819C211yesmaximal, characteristic
2D4×#11758194C211yesmaximal, characteristic, complemented
3#21446737C211yesmaximal, characteristic, complemented
4#21444271C211yesmaximal, characteristic, complemented
5#21443722C211yesmaximal, characteristic, complemented
6#21443656C211yesmaximal, characteristic, complemented
7C4×#102×C61C211yesmaximal, characteristic, complemented
8C22×#11758194—21no—
9#16840312C2211yescharacteristic
10#16840075—21no—
11#16840042C411yescharacteristic, complemented
12#16840042C411yescharacteristic, complemented
13#16839957C411yescharacteristic, complemented
14#16839957C411yescharacteristic, complemented
15#16839896—21no—
16C4×#11758199—21no—
17C4×#11758199—21no—
18#16839840—21no—
19#16839834—22no—
20D4×#92418—21no—
21#16839815C2211yescharacteristic
22#16839786C2211yescharacteristic
23C2×#14519705—21no—
24C2×#14519705—21no—
25#16839726—21no—
26C4×#11758194C2211yescharacteristic
27#16839491—22no—
28C2×C4×D4×C61C2211yescharacteristic
29C2×#102×C61—21no—
30C2×C4×C8×C61C2211yescharacteristic
31C4×C4⋊C4×C61C2211yescharacteristic
32C61×#340—21no—
33C2×#11758222—21no—
34C2×#11758199—21no—
35C2×#11758199—21no—
36C2×#11758194—22no—
37C2×#11758194—21no—
38C2×#11758194—42no—
39C2×#11758194—42no—
40C2×#11758194D411yescharacteristic
41C2×#11758194D411yescharacteristic
42C22×#92418—22no—
43#14519777C2×C411yescharacteristic
44#14519774C2×C411yescharacteristic
45#14519765—21no—
46#14519751—21no—
47#14519751—21no—
48C4×D244—21no—
49C4×D244—21no—
50#14519710—21no—
51#14519710—21no—
52C4⋊#92418—21no—
53C4⋊#92418C2×C411yescharacteristic
54C4⋊#92418C2×C411yescharacteristic
55C4⋊#92418D412yes—
56#14519705—42no—
57#14519705—42no—
58#14519698—21no—
59#14519698—21no—
60#14519697—21no—
61#14519697—21no—
62C22⋊#92418—22no—
63C22⋊#92418—22no—
64C22⋊#92418—21no—
65#14519688—21no—
66C4×#92418—21no—
67C4×#92418—21no—
68C22×D4×C61D411yescharacteristic
69C23×C4×C61—21no—
70C22×C8×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C4×D4×C61C2×C411yescharacteristic
74C4×D4×C61C2×C411yescharacteristic
75C4×D4×C61D411yescharacteristic
76C4×D4×C61D411yescharacteristic
77C2×C4⋊C4×C61—21no—
78C2×C4⋊C4×C61D411yescharacteristic
79C2×C22⋊C4×C61—21no—
80C2×C42×C61—21no—
81C2×C42×C61C2311yescharacteristic
82#102×C61—24no—
83C4×C8×C61—21no—
84C4×C8×C61—21no—
85#95×C61—21no—
86C24×C61—21no—
87C2×D4×C61—22no—
88C2×D4×C61—21no—
89C2×D4×C61—41no—
90C2×D4×C61C22⋊C411yescharacteristic
91C2×D4×C61C22⋊C411yescharacteristic
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61#4111yescharacteristic
105C2×C22⋊D61—41no—
106#11758222—41no—
107#11758222—41no—
108#11758222—41no—
109#11758222—41no—
110C2×D244—21no—
111C2×D244—21no—
112C2×D244—21no—
113C2×C4×D61—41no—
114C2×Dic122—21no—
115C2×C8×C61—22no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—22no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61C22⋊C411yescharacteristic
122C4⋊C4×C61C22⋊C411yescharacteristic
123C22⋊C4×C61—21no—
124C22⋊C4×C61—21no—
125C22⋊C4×C61—21no—
126C22⋊C4×C61—21no—
127C42×C61—41no—
128C42×C61—41no—
129C42×C61C22×C411yescharacteristic
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61#4111yescharacteristic
133#11758199—42no—
134#11758199—42no—
135#11758198—41no—
136#11758198—41no—
137C4⋊Dic61—21no—
138C4⋊Dic61—21no—
139#11758194—21no—
140#11758194—21no—
141#11758194—21no—
142#11758194—44no—
143#11758194—41no—
144#11758194—41no—
145#11758194D812yescomplemented
146C2×#92418—21no—
147C2×#92418—21no—
148C2×#92418—21no—
149C2×#92418—21no—
150C2×#92418—22no—
151C2×#92418—44no—
152C23×C61—21no—
153C23×C61—21no—
154C23×C61—42no—
155C23×C61—41no—
156C23×C61—41no—
157C23×C61—81no—
158C23×C61#12111yescharacteristic
159C22×D61—41no—
160D4×C61—21no—
161D4×C61—21no—
162D4×C61—21no—
163D4×C61—42no—
164D4×C61#10412yescomplemented
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—42no—
181C2×C4×C61—81no—
182C2×C4×C61—81no—
183C2×C4×C61C2×C22⋊C411yescharacteristic
184C2×C4×C61C4×D411yescharacteristic
185C2×C4×C61C4×D411yescharacteristic
186C2×C4×C61#12011yescharacteristic
187C2×C4×C61#12111yescharacteristic
188C2×C4×C61#12311yescharacteristic
189C2×C4×C61C2×D811yescharacteristic
190C2×C4×C61#13511yescharacteristic
191C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
193C22⋊D61—81no—
194C22⋊D61—81no—
195C2×Dic61—41no—
196D244—42no—
197D244—41no—
198D244—41no—
199D244—41no—
200D244—41no—
201C4×D61—81no—
202C4×D61—81no—
203Dic122—41no—
204Dic122—41no—
205C8×C61—42no—
206#92418—22no—
207#92418—41no—
208#92418—41no—
209#92418—42no—
210#92418—41no—
211#8991—611nomaximal, Sylow
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—22no—
215C22×C61—41no—
216C22×C61—41no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61—41no—
220C22×C61—82no—
221C22×C61—82no—
222C22×C61#38611yescharacteristic
223C22×C61#45911yescharacteristic
224C22×C61#46311yescharacteristic
225C2×D61—81no—
226C2×D61—81no—
227C2×D61—81no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—41no—
232C4×C61—41no—
233C4×C61—82no—
234C4×C61C2×#10411yescharacteristic
235C4×C61#42111yescharacteristic
236C4×C61C4×D811yescharacteristic
237C4×C61#44211yescharacteristic
238C4×C61#44711yescharacteristic
239C4×C61#44911yescharacteristic
240Dic61—81no—
241#3100—611no—
242D4×M16—611no—
243#1980—611no—
244C4×#102D6111yescharacteristic, complemented
245#1492—611no—
246#1303—611no—
247#1278—611no—
248C2×C61—21no—
249C2×C61—21no—
250C2×C61—42no—
251C2×C61—81no—
252C2×C61#187111yescharacteristic
253C2×C61#187911yescharacteristic
254C2×C61#188111yescharacteristic
255D61—161no—
256C22×M16—1221no—
257#532—611no—
258C2×C4×D4C2×D6111yescharacteristic
259#480—1221no—
260#474—611no—
261#474—611no—
262#459—611no—
263#459—611no—
264#447—1221no—
265C4×D8—1221no—
266C4×D8—1221no—
267#436—1221no—
268#435—1222no—
269C8×D4—1221no—
270#431—611no—
271#423—611no—
272C2×#104—1221no—
273C2×#104—1221no—
274C2×#102—21no—
275#407—1221no—
276C4×M16—611no—
277C2×C4×C8C2×D6111yescharacteristic
278C4×C4⋊C4C2×D6111yescharacteristic
279#340—21no—
280D4⋊C8—1222no—
281C61#899111yescharacteristic, complemented, Sylow
282C2×#41—1221no—
283C22×D4C22⋊D6111yescharacteristic
284C23×C4—21no—
285C2×D8—1221no—
286C2×D8—1221no—
287C2×M16—611no—
288C2×M16—611no—
289C2×M16—1222no—
290C2×M16—1221no—
291C2×M16—2442no—
292C2×M16—2442no—
293C22×C8—21no—
294C22×C8—1222no—
295C4⋊Q8—611no—
296#127—611no—
297#124—1221no—
298#121—1221no—
299#121—1221no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—1221no—
303C4×D4—1221no—
304C4×D4C4×D6111yescharacteristic
305C4×D4C4×D6111yescharacteristic
306C4×D4D24411yescharacteristic
307C4×D4D24411yescharacteristic
308C2×C4⋊C4—21no—
309C2×C4⋊C4C22⋊D6111yescharacteristic
310C2×C22⋊C4—21no—
311C2×C42—21no—
312C2×C42C22×D6111yescharacteristic
313#107—1221no—
314#107—1221no—
315C4⋊C8—611no—
316C4⋊C8—611no—
317C4⋊C8—612no—
318C4⋊C8—1221no—
319#104—2442no—
320#104—2442no—
321#102—24no—
322#102—1221no—
323#102—1221no—
324#102—1221no—
325#102—1221no—
326C22⋊C8—1222no—
327C22⋊C8—1222no—
328C22⋊C8—1221no—
329#97—1221no—
330C4×C8—21no—
331C4×C8—21no—
332C4×C8—1221no—
333C4×C8—1221no—
334#95—21no—
335C24—21no—
336#41—2441no—
337#41—2441no—
338#41—2441no—
339#41—2441no—
340C2×Q8—1221no—
341C2×D4—22no—
342C2×D4—21no—
343C2×D4—41no—
344C2×D4—1221no—
345C2×D4—1221no—
346C2×D4—1221no—
347C2×D4—2441no—
348C2×D4#1175819811yescharacteristic
349C2×D4#1175819811yescharacteristic
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—2441no—
361C22×C4D4×D6111yescharacteristic
362C22×C4#1175822411yescharacteristic
363C22×C4C2×C22⋊D6111yescharacteristic
364D8—2442no—
365D8—2442no—
366M16—612no—
367M16—1221no—
368M16—1221no—
369M16—1221no—
370M16—2444no—
371M16—2441no—
372M16—2441no—
373C2×C8—22no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—1221no—
377C2×C8—1221no—
378C2×C8—1221no—
379C2×C8—1221no—
380C2×C8—1222no—
381C2×C8—2444no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—41no—
385C4⋊C4—1221no—
386C4⋊C4—1221no—
387C4⋊C4#1175819811yescharacteristic
388C4⋊C4#1175819811yescharacteristic
389C22⋊C4—21no—
390C22⋊C4—21no—
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—2441no—
394C22⋊C4—2441no—
395C42—41no—
396C42—41no—
397C42C2×C4×D6111yescharacteristic
398C42C2×D24411yescharacteristic
399C42D4×D6111yescharacteristic
400C42#1175822411yescharacteristic
401C23—21no—
402C23—21no—
403C23—42no—
404C23—41no—
405C23—41no—
406C23—81no—
407C23—2441no—
408C23#1451974911yescharacteristic
409Q8—2441no—
410Q8—2441no—
411D4—21no—
412D4—21no—
413D4—21no—
414D4—42no—
415D4—4881no—
416D4—4881no—
417D4—2442no—
418D4—2441no—
419D4—2441no—
420D4—2441no—
421D4—2441no—
422D4#1451970512yescomplemented
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—4881no—
442C2×C4—4881no—
443C2×C4—2441no—
444C2×C4C2×#1175819811yescharacteristic
445C2×C4#1451973711yescharacteristic
446C2×C4#1451973711yescharacteristic
447C2×C4#1451974711yescharacteristic
448C2×C4#1451974911yescharacteristic
449C2×C4#1451976111yescharacteristic
450C2×C4D8×D6111yescharacteristic
451C2×C4#1451979811yescharacteristic
452C2×C4#1451980111yescharacteristic
453C2×C4#1451980411yescharacteristic
454C8—42no—
455C8—1222no—
456C8—2441no—
457C8—2441no—
458C8—2442no—
459C8—2441no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—82no—
469C22—82no—
470C22—4881no—
471C22—4881no—
472C22—4881no—
473C22#1683963911yescharacteristic
474C22#1683995511yescharacteristic
475C22#1683997911yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—41no—
480C4—41no—
481C4—82no—
482C4—4881no—
483C4C2×#1451970511yescharacteristic
484C4#1683978011yescharacteristic
485C4#1683984211yescharacteristic
486C4#1683987111yescharacteristic
487C4#1683989711yescharacteristic
488C4#1683990811yescharacteristic
489C2—21no—
490C2—21no—
491C2—42no—
492C2—81no—
493C2—9761no—
494C2#2144611911yescharacteristic
495C2#2144616511yescharacteristic
496C2#2144617911yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC4×#102×C61C2
socleC22×C61#386
prime radical#21455819C2
cosocleC2×C42×C61C23
hypercenterC4×#102D61
hypocenterC61#8991
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#102

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. D4×#11758194C2semidirect
3. #21446737C2semidirect
4. #21444271C2semidirect
5. #21443722C2semidirect
6. #21443656C2semidirect
7. C4×#102×C61C2semidirect
11. #16840042C4semidirect
12. #16840042C4semidirect
13. #16839957C4semidirect
14. #16839957C4semidirect
145. #11758194D8semidirect
164. D4×C61#104semidirect
244. C4×#102D61semidirect
281. C61#8991semidirect
422. D4#14519705semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214558192
D4×#117581942
#214467372
#214442712
#214437222
#214436562
C4×#102×C612
#899161